plz answer me in detail thx a lott!

4. In this exercise we consider the \" Hanging the Whiteboard Up\" game from class. The one-stage game has the following payoffs: (a) L M R U 0,0 3,4 6,0 M 4,3 0,0 00 D 0,0 0,0 5,5 First we consider the multistage game, where the \" Hanging the Whiteboard Up\" is repeated 2 times, as in class. Suppose that each player's payoff function in the multi-stage game is the sum of his or her discounted payoffs in the two periods. Consider the following strategy: \"Play (D, R) in the first stage. If the rststage outcome is (D, R), then play (M, L) in the second stage; if the rst-stage outcome is not (D, R), then play ((gU, $4M), (2L, $314)) in the second stage.\" Give the range for which discount factors 6 this strategy is a subgame perfect Nash equilibrium. Now consider the innite-horizon version of the repeated game. Give a strategy and compute the smallest discount factor in order for a social optimum cooperating subgameperfect equilibrium to exist. Remember that the social optimum outcome happens when the sum of all players' payoffs is as high as possible. [2 + 3 = 5 Points]